Common Core Initiative
What connection exists between arithmetic and geometric sequences and linear and exponential functions?
Students have already had experience with arithmetic and geometric sequences. As they studied linear and exponential functions these sequences appeared in tabular representations; this unit will allow students to formalize this knowledge. Students will take NOW-NEXT recursive equations and write them using subscripted notation. Students will learn to model problems involving sequential change, represent them using sigma notation, and analyze their model to solve problems. Understanding the differences and characteristics of arithmetic and geometric sequences will help students develop strategies to find sums of arithmetic and geometric series and develop formulas for these sums. Technology in the form of sequential mode of graphing calculators, CAS systems, and computer spreadsheets will provide additional resources for students to explore these topics.
There are standards listed in this section for two reasons.
Modified For this Unit
n/a
Developed and/or Utilized Across Multiple Units
Linear, Quadratic, and Exponential Models
HSF-LE.A. Construct and compare linear and exponential models and solve problems.
HSF-LE.A.1b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
HSF-LE.A.1c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
arithmetic sequence
arithmetic series
convergence
divergence
explicit formulas
finite series
geometric sequence
geometric series
infinite series
nth term
recursive formulas
subscripted notation
sum of a series
summation/sigma notation
Standards for Mathematical Practice
Students will have opportunities to: